Zeta functions of supersingular curves of genus 2

Daniel Maisner, Enric Nart

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

We determine which isogeny classes of supersingular abelian surfaces over a finite field k of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to k-isomorphism, leading to the same zeta function. © Canadian Mathematical Society 2007.
Original languageEnglish
Pages (from-to)372-392
JournalCanadian Journal of Mathematics
Volume59
DOIs
Publication statusPublished - 1 Jan 2007

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